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Rigorous Coupled-wave Analysis
Rigorous coupled-wave analysis (RCWA) is a semi-analytical method in computational electromagnetics that is most typically applied to solve scattering from periodic dielectric structures. It is a Fourier-space method so devices and fields are represented as a sum of spatial harmonics. Floquet's theorem The method is based on Floquet's theorem that the solutions of periodic differential equations can be expanded with Floquet functions (or sometimes referred as Bloch wave, especially in solid-state physics community). A device is divided into layers that are each uniform in the z direction. A staircase approximation is needed for curved devices with properties such as dielectric permittivity graded along the z-direction. The electromagnetic modes in each layer are calculated and analytically propagated through the layers. The overall problem is solved by matching boundary conditions at each of the interfaces between the layers using a technique like scattering matrices. To s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Electromagnetics
Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment. It typically involves using computer programs to compute approximate solutions to Maxwell's equations to calculate antenna performance, electromagnetic compatibility, radar cross section and electromagnetic wave propagation when not in free space. A large subfield is ''antenna modeling'' computer programs, which calculate the radiation pattern and electrical properties of radio antennas, and are widely used to design antennas for specific applications. Background Several real-world electromagnetic problems like electromagnetic scattering, electromagnetic radiation, modeling of waveguides etc., are not analytically calculable, for the multitude of irregular geometries found in actual devices. Computational numerical techniques can overcome the inability to derive closed f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floquet's Theorem
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form :\dot = A(t) x, with \displaystyle A(t) a piecewise continuous periodic function with period T and defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to , gives a canonical form for each fundamental matrix solution of this common linear system. It gives a coordinate change \displaystyle y=Q^(t)x with \displaystyle Q(t+2T)=Q(t) that transforms the periodic system to a traditional linear system with constant, real coefficients. When applied to physical systems with periodic potentials, such as crystals in condensed matter physics, the result is known as Bloch's theorem. Note that the solutions of the linear differential equation form a vector space. A matrix \phi\,(t) is called a '' fundamental matrix solution'' if all columns are linearly independent solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bloch Wave
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential take the form of a plane wave modulated by a periodic function. The theorem is named after the physicist Felix Bloch, who discovered the theorem in 1929. Mathematically, they are written where \mathbf is position, \psi is the wave function, u is a periodic function with the same periodicity as the crystal, the wave vector \mathbf is the crystal momentum vector, e is Euler's number, and i is the imaginary unit. Functions of this form are known as Bloch functions or Bloch states, and serve as a suitable basis for the wave functions or states of electrons in crystalline solids. Named after Swiss physicist Felix Bloch, the description of electrons in terms of Bloch functions, termed Bloch electrons (or less often ''Bloch Waves''), underlies the concept of electronic band structures. These eigenstates are written with subscripts as \psi_, where n is a discret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid-state Physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors. Background Solid materials are formed from densely packed atoms, which interact intensely. These interactions produce the mechanical (e.g. hardness and Elasticity (physics), elasticity), Heat conduction, thermal, Electrical conduction, electrical, Magnetism, magnetic and Crystal optics, optical properties of solids. Depending on the material involved and the conditions in which it was formed, the atoms may be arranged in a regular, geometric pattern (crystal, crystalline solids, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell's Equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.''Electric'' and ''magnetic'' fields, according to the theory of relativity, are the components of a single electromagnetic field. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern form of the equations in their most common formul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Phenomenon
In mathematics, the Gibbs phenomenon, discovered by Available on-line at:National Chiao Tung University: Open Course Ware: Hewitt & Hewitt, 1979. and rediscovered by , is the oscillatory behavior of the Fourier series of a piecewise continuously differentiable periodic function around a jump discontinuity. The function's Nth partial Fourier series (formed by summing its N lowest constituent sinusoids) produces large peaks around the jump which overshoot and undershoot the function's actual values. This approximation error approaches a limit of about 9% of the jump as more sinusoids are used, though the infinite Fourier series sum does eventually converge almost everywhere except the point of discontinuity. The Gibbs phenomenon was observed by experimental physicists, but was believed to be due to imperfections in the measuring apparatus, and it is one cause of ringing artifacts in signal processing. Description The Gibbs phenomenon involves both the fact that Fourier su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Semiconductor Device
A power semiconductor device is a semiconductor device used as a switch or rectifier in power electronics (for example in a switch-mode power supply). Such a device is also called a power device or, when used in an integrated circuit, a power IC. A power semiconductor device is usually used in "commutation mode" (i.e., it is either on or off), and therefore has a design optimized for such usage; it should usually not be used in linear operation. Linear power circuits are widespread as voltage regulators, audio amplifiers, and radio frequency amplifiers. Power semiconductors are found in systems delivering as little as a few tens of milliwatts for a headphone amplifier, up to around a gigawatt in a high voltage direct current transmission line. History The first electronic device used in power circuits was the electrolytic rectifier - an early version was described by a French experimenter, A. Nodon, in 1904. These were briefly popular with early radio experimenters as they c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forouhi–Bloomer Model
The Forouhi–Bloomer model is a mathematical formula for the frequency dependence of the complex-valued refractive index. The model can be used to fit the refractive index of amorphous and crystalline semiconductor and dielectric materials at energies near and greater than their optical band gap. The dispersion relation bears the names of Rahim Forouhi and Iris Bloomer, who created the model and interpreted the physical significance of its parameters. The model is aphysical due to its incorrect asymptotic behavior and non-Hermitian character. These shortcomings inspired modified versions of the model as well as development of the Tauc–Lorentz model. Mathematical Formulation The complex refractive index is given by : \tilde(E) = n(E) + i \kappa(E) where * n is the real component of the complex refractive index, commonly called the refractive index, * \kappa is the imaginary component of the complex refractive index, commonly called the extinction coefficient, * E is the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solar Cell
A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.Solar Cells chemistryexplained.com It is a form of photoelectric cell, defined as a device whose electrical characteristics, such as , , or resistance, vary when exposed to light. Individual solar cell devices are often the electrical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solar Panel
A solar cell panel, solar electric panel, photo-voltaic (PV) module, PV panel or solar panel is an assembly of photovoltaic solar cells mounted in a (usually rectangular) frame, and a neatly organised collection of PV panels is called a photovoltaic system or solar array. Solar panels capture sunlight as a source of radiant energy, which is converted into electric energy in the form of direct current (DC) electricity. Arrays of a photovoltaic system can be used to generate solar electricity that supplies electrical equipment directly, or grid-connected photovoltaic system, feeds power back into an alternate current (AC) electric grid, grid via an solar inverter, inverter system. History In 1839, the ability of some materials to create an electrical charge from light exposure was first observed by the French physicist Edmond Becquerel. Though these initial solar panels were too inefficient for even simple electric devices, they were used as an instrument to measure light. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OPTOS Formalism
OPTOS (optical properties of textured optical sheets) is a simulation formalism for determining optical properties of sheets with plane-parallel structured interfaces. The method is versatile as interface structures of different optical regimes, e.g. geometrical and wave optics, can be included. It is very efficient due to the re-usability of the calculated light redistribution properties of the individual interfaces. It has so far been mainly used to model optical properties of solar cells and solar modules but it is also applicable for example to LEDs or OLEDs with light extraction structures. History The development of the OPTOS formalism started in 2015 at the Fraunhofer Institute for Solar Energy Systems ISE in Freiburg, Germany. The mathematical formulation has been described in detail in several open access publications. Tucher, N.; Eisenlohr, J.; Kiefel, P.; Höhn, O.; Hauser, H.; Peters, M.; Müller, C.; Goldschmidt, J. C.; Bläsi, B. "3D optical simulation formalism OPTO ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics). Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods. Classical mechanics The rigorous, abstract and advanced reformulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics and lead to understanding the deep interplay of the notions of symmetry (physics), symmetry and conservation law, con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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